Base field 4.4.16225.1
Generator \(w\), with minimal polynomial \(x^{4} - x^{3} - 13x^{2} + 6x + 36\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[1, 1, 1]$ |
| Dimension: | $6$ |
| CM: | no |
| Base change: | yes |
| Newspace dimension: | $6$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{6} - 11x^{4} + 21x^{2} - 3\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 4 | $[4, 2, \frac{1}{3}w^{3} - \frac{4}{3}w^{2} - \frac{4}{3}w + 6]$ | $\phantom{-}e$ |
| 4 | $[4, 2, -\frac{1}{3}w^{3} - \frac{2}{3}w^{2} + \frac{10}{3}w + 7]$ | $\phantom{-}e$ |
| 9 | $[9, 3, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{7}{2}w - 9]$ | $\phantom{-}\frac{1}{2}e^{4} - 5e^{2} + \frac{11}{2}$ |
| 9 | $[9, 3, \frac{1}{3}w^{3} + \frac{2}{3}w^{2} - \frac{7}{3}w - 5]$ | $\phantom{-}\frac{1}{2}e^{4} - 5e^{2} + \frac{11}{2}$ |
| 11 | $[11, 11, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{1}{6}w]$ | $-e^{5} + 10e^{3} - 13e$ |
| 19 | $[19, 19, w + 1]$ | $\phantom{-}e^{5} - 11e^{3} + 20e$ |
| 19 | $[19, 19, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{13}{6}w + 2]$ | $\phantom{-}e^{5} - 11e^{3} + 20e$ |
| 25 | $[25, 5, -\frac{1}{3}w^{3} + \frac{1}{3}w^{2} + \frac{7}{3}w - 1]$ | $\phantom{-}e^{2} + 1$ |
| 29 | $[29, 29, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{13}{6}w]$ | $-\frac{1}{2}e^{5} + 6e^{3} - \frac{29}{2}e$ |
| 29 | $[29, 29, w - 1]$ | $-\frac{1}{2}e^{5} + 6e^{3} - \frac{29}{2}e$ |
| 31 | $[31, 31, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w + 3]$ | $-e^{3} + 7e$ |
| 31 | $[31, 31, \frac{1}{6}w^{3} - \frac{1}{6}w^{2} - \frac{1}{6}w + 2]$ | $-e^{3} + 7e$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} - \frac{1}{2}w^{2} + \frac{9}{2}w + 5]$ | $-\frac{3}{2}e^{5} + 16e^{3} - \frac{55}{2}e$ |
| 41 | $[41, 41, -\frac{1}{2}w^{3} + \frac{3}{2}w^{2} + \frac{5}{2}w - 8]$ | $-\frac{3}{2}e^{5} + 16e^{3} - \frac{55}{2}e$ |
| 59 | $[59, 59, \frac{1}{3}w^{3} - \frac{1}{3}w^{2} - \frac{10}{3}w - 1]$ | $-e^{4} + 8e^{2} - 3$ |
| 59 | $[59, 59, -\frac{1}{3}w^{3} + \frac{4}{3}w^{2} + \frac{7}{3}w - 7]$ | $-e^{4} + 8e^{2} - 3$ |
| 59 | $[59, 59, \frac{1}{2}w^{3} - \frac{1}{2}w^{2} - \frac{5}{2}w + 2]$ | $-e^{4} + 8e^{2} - 3$ |
| 79 | $[79, 79, w^{2} - 11]$ | $-e^{4} + 9e^{2} - 8$ |
| 79 | $[79, 79, \frac{1}{6}w^{3} - \frac{7}{6}w^{2} - \frac{7}{6}w + 3]$ | $-e^{4} + 9e^{2} - 8$ |
| 89 | $[89, 89, -\frac{1}{6}w^{3} + \frac{1}{6}w^{2} + \frac{19}{6}w - 5]$ | $\phantom{-}\frac{5}{2}e^{5} - 27e^{3} + \frac{91}{2}e$ |
Atkin-Lehner eigenvalues
This form has no Atkin-Lehner eigenvalues since the level is \((1)\).